Non-stationary Spatio-Temporal Modeling of COVID-19 Progression in The US

Yue Bai, Abolfazl Safikhani, George Michailidis

Abstract:

The fast transmission rate of COVID-19 worldwide has made this virus the most important
challenge of year 2020. Many mitigation policies have been imposed by the governments at different
regional levels (country, state, county, and city) to stop the spread of this virus. Quantifying the effect
of such mitigation strategies on the transmission and recovery rates, and predicting the rate of new
daily cases are two crucial tasks. In this paper, we propose a modeling framework which not only
accounts for such policies but also utilizes the spatial and temporal information to characterize the
pattern of COVID-19 progression. Specifically, a piecewise susceptible-infected-recovered (SIR) model
is developed while the dates at which the transmission/recover rates change significantly are defined as
“break points” in this model. A novel and data-driven algorithm is designed to locate the break points
using ideas from fused lasso and thresholding. In order to enhance the forecasting power and to describe
additional temporal dependence among the daily number of cases, this model is further coupled with
spatial smoothing covariates and vector auto-regressive (VAR) model. The proposed model is applied
to several U.S. states and counties, and the results confirm the effect of “stay-at-home orders” and
some states’ early “re-openings” by detecting break points close to such events. Further, the model
performed satisfactorily short-term forecasts of the number of new daily cases at regional levels by
utilizing the estimated spatio-temporal covariance structures. Finally, some theoretical results and
empirical performance of the proposed method